Pair Selection

To look for candidate metabolite-methylation pairs, I ran three linear models and selected based on the p value cutoffs below (e.g. metabolite and methylation associated at p < 0.01, and both associated with IA status at p < 0.01).

Using this mediation structure, there were 1490 pairs selected with 58 unique metabolites.

feature name
gctof_214 5930
hilic_32 Histidine
hilic_92 Unknown
hilic_100 Unknown
hilic_113 Unknown
hilic_148 Unknown
hilic_156 Unknown
hilic_174 Unknown
hilic_176 Unknown
hilic_195 Unknown
hilic_200 Unknown
hilic_245 Unknown
hilic_251 Unknown
hilic_271 Unknown
hilic_273 Unknown
hilic_275 Unknown
hilic_307 Unknown
hilic_346 Unknown
hilic_357 Unknown
hilic_368 Unknown
hilic_385 Unknown
hilic_386 Unknown
hilic_387 Unknown
hilic_388 Unknown
hilic_390 Unknown
hilic_391 Unknown
hilic_467 Unknown
hilic_483 Unknown
hilic_528 Unknown
hilic_697 Unknown
hilic_714 Unknown
hilic_724 Unknown
hilic_725 Unknown
hilic_726 Unknown
hilic_750 Unknown
hilic_759 Unknown
hilic_904 Unknown
hilic_996 Unknown
hilic_997 Unknown
lipid_111 PC (p-32:0) or PC (o-32:1)
lipid_143 PE (38:4)
lipid_154 SM (d34:2)
lipid_428 Unknown
lipid_435 Unknown
lipid_445 Unknown
lipid_685 SM (d34:2) [M+HAc-H]- & [M+Cl]- _YLWSJLLZUHSIEA-CKSUKHGVSA-N
lipid_711 CSH_negESI #569
lipid_719 CSH_negESI #690
lipid_775 Unknown
lipid_798 Unknown
lipid_801 Unknown
lipid_819 Unknown
lipid_846 Unknown
lipid_855 Unknown
lipid_865 Unknown
lipid_890 Unknown
lipid_992 Unknown
lipid_1111 Unknown

Using this mediation structure, there were 600 pairs selected with 23 unique metabolites.

feature name
hilic_61 PC(38:4)
hilic_345 Unknown
hilic_378 Unknown
hilic_380 Unknown
hilic_397 Unknown
hilic_816 Unknown
hilic_877 Unknown
hilic_975 Unknown
hilic_1012 Unknown
lipid_22 CE (20:3)
lipid_294 Unknown
lipid_329 Unknown
lipid_386 Unknown
lipid_429 Unknown
lipid_494 Unknown
lipid_528 Unknown
lipid_563 FA (12:0) [M-H]- (lauric acid)_POULHZVOKOAJMA-UHFFFAOYSA-N
lipid_568 FA (16:0) [M-H]- (palmitic acid)_IPCSVZSSVZVIGE-UHFFFAOYSA-N
lipid_572 FA (18:0) [M-H]- (stearic acid)_QIQXTHQIDYTFRH-UHFFFAOYSA-N
lipid_856 Unknown
lipid_925 Unknown
lipid_931 Unknown

Mediation Analysis

Methylation at PSV

Models

Terms:

\[ Y = \text{IA Status}\\ M = \text{Metabolite at SV}\\ T = \text{Methylation at PSV}\\ X_2 = \text{Sex}\\ X_3 = \text{DR3/4 Status}\\ X_4 = \text{Age at PSV}\\ X_5 = \text{Time from PSV to SV}\\ \text{i indexes subject}\\ \]

Mediator Model

\[ M_i = \beta_0 + \beta_1 T_i+\beta_2'C+\epsilon_i\\ \text{With } \epsilon_i\text{ i.i.d. } N(0,\sigma^2) \]

In order to account for the case control design, the mediator model is fit to only the control subjects. The nature of case controls studies means that the cases are over-sampled compared to controls. The regression parameters in the outcome model are consistently estimated in logistic regression, but the study design needs to be taken into account in the mediator model. Fitting this model using only the controls is a good approximation for the regression coefficients that would be obtained in a cohort study, assuming the outcome is rare and that inclusion in the study depends only on the outcome (and not the mediator or exposure).

Outcome Model

\[ \text{Let }p=\text{the probability a given subject is an IA case}=P(Y = 1)\\ ln(\frac{p}{1-p}) = \theta_0 +\theta_1 T_i+\theta_2 M_i+\theta_3(T_i*M_i)+\theta_4'C \]

Where \(\beta_2'\) and \(\theta_4'\) are vectors of estimates for multiple confounders \(C\).

Mediation

CDE is the controlled direct effect. This is how much the outcome would change on average if the mediator was fixed (at m) across the whole population, and the “treatment” (exposure) changed from 0 to 1.

NDE is the natural direct effect. It represents the average change in outcome if the “exposure” changed from 0 to 1, and each individual’s value for the mediator varied as it normally would (in the absence of the exposure). In other words, it is the effect of the exposure on the outcome that would remain if the path from exposure to mediator was removed.

NIE is the natural indirect effect. It is the average change in outcome if the exposure was fixed at 1, but “the mediator were changed from the level it would take if \(t^*=0\) to the level it would take if \(t=1\).” This is essentially the effect of the exposure on the outcome that operates through changing the mediator.

Note, if the interaction term is 0, both the CDE and NDE are equal to the direct effect under Baron and Kenny’s formulation. Also, while CDE, NDE, and NIE are interpreted on the odds scale, proportion mediated is interpreted on the risk scale.

\[ OR^{CDE}(m)=exp(\theta_1+\theta_3 m)\\ OR^{NDE}=exp((\theta_1+\theta_3\beta_0+\theta_3\beta_1+\theta_3\beta_2'C+\theta_3\theta_2\sigma^2)+0.5\theta_3^2\sigma^2)\\ OR^{NIE}=exp(\theta_2\beta_1+\theta_3\beta_1)\\ \text{Proportion mediated (PM)}=\frac{OR^{NDE}(OR^{NIE}-1)}{(OR^{NDE}*OR^{NIE}-1)} \]

Results

In the regmedint summary table, “pure natural direct effect (pnde) is what is typically called the natural direct effect (NDE). The total natural indirect effect (tnie) is the corresponding natural indirect effect (NIE).” link

Because proportion mediated is a highly variables measure and is problematic when the NDE and NIE are in opposite directions, it is generally best to use the estimate and confidence interval for the NIE instead (pg. 48).

Methylation at PSV

There are 52 pairs with significant NIE:

Pair NIE
cg26981432 & hilic_467 46046705.625
cg02223028 & hilic_32 9448231.479
cg23110027 & lipid_711 7881.339
cg18576552 & hilic_697 6191.422
cg17350432 & hilic_32 4324.847
cg07375207 & hilic_176 4169.481
cg16466870 & hilic_996 2677.473
cg24328676 & hilic_174 1655.612
cg07375207 & hilic_174 672.019
cg15740979 & hilic_996 603.111
cg07601148 & hilic_996 556.959
cg15052330 & hilic_32 254.879
cg07601148 & hilic_174 243.600
cg21040069 & lipid_1111 226.982
cg02647297 & lipid_775 144.116
cg07375207 & hilic_32 68.407
cg01709543 & lipid_775 60.760
cg00390143 & lipid_711 30.334
cg07064673 & hilic_32 28.068
cg00390143 & lipid_685 21.408
cg01604946 & lipid_111 18.519
cg09371112 & hilic_174 15.768
cg14410733 & lipid_819 14.930
cg00390143 & lipid_775 9.155
cg14894245 & hilic_904 5.735
cg12616177 & hilic_346 2.030
cg03130816 & hilic_113 1.791
cg27578381 & hilic_251 0.797
cg01042202 & hilic_271 0.712
cg19083626 & hilic_483 0.703
cg19916129 & hilic_467 0.693
cg15142694 & hilic_307 0.615
cg23120936 & hilic_174 0.603
cg16727231 & hilic_271 0.595
cg19083626 & hilic_176 0.559
cg19916129 & hilic_176 0.498
cg08013331 & lipid_890 0.424
cg26612794 & hilic_996 0.407
cg19939773 & hilic_32 0.405
cg20453969 & hilic_176 0.381
cg13649728 & hilic_113 0.271
cg16362592 & hilic_391 0.107
cg00546307 & hilic_271 0.096
cg06320277 & hilic_195 0.064
cg00546307 & hilic_251 0.059
cg04229103 & hilic_346 0.002
cg23466054 & hilic_357 0.001
cg20176194 & hilic_32 0.000
cg27107970 & hilic_245 0.000
cg15130211 & hilic_32 0.000
cg08882882 & lipid_992 0.000
cg24282826 & lipid_711 0.000

Data issues

I think that the problem here is the fact that the metabolites and methylation values are on very different scales, so when you’re multiplying the \(\beta\) values they can occasionally blow up.

When the methylation values are also scaled, the NIE value is much more reasonable:

x
cde 0.3715006
pnde 0.9835381
tnie 0.7118551
tnde 0.8236703
pnie 0.8500204
te 0.7001366

Same again for the next pair:

x
cde 1.1786950
pnde 1.5285937
tnie 0.5709904
tnde 1.2064693
pnie 0.7234434
te 0.8728123

Annotation

feature name
318 hilic_32 Histidine
399 hilic_113 Unknown
460 hilic_174 Unknown
462 hilic_176 Unknown
481 hilic_195 Unknown
531 hilic_245 Unknown
537 hilic_251 Unknown
557 hilic_271 Unknown
593 hilic_307 Unknown
632 hilic_346 Unknown
643 hilic_357 Unknown
677 hilic_391 Unknown
753 hilic_467 Unknown
769 hilic_483 Unknown
983 hilic_697 Unknown
1190 hilic_904 Unknown
1282 hilic_996 Unknown
1429 lipid_111 PC (p-32:0) or PC (o-32:1)
2003 lipid_685 SM (d34:2) [M+HAc-H]- & [M+Cl]- _YLWSJLLZUHSIEA-CKSUKHGVSA-N
2029 lipid_711 CSH_negESI #569
2093 lipid_775 Unknown
2137 lipid_819 Unknown
2208 lipid_890 Unknown
2310 lipid_992 Unknown
2429 lipid_1111 Unknown
chr pos Name Probe_rs Relation_to_Island UCSC_RefGene_Name
cg00546307 chr1 1946355 cg00546307 NA OpenSea
cg03130816 chr1 39456103 cg03130816 rs4422996 N_Shore AKIRIN1;AKIRIN1
cg15052330 chr2 72360243 cg15052330 NA OpenSea CYP26B1
cg06320277 chr2 105980029 cg06320277 NA OpenSea FHL2;FHL2;FHL2;FHL2
cg04229103 chr2 145090268 cg04229103 NA Island GTDC1
cg20176194 chr2 220173205 cg20176194 NA Island PTPRN
cg15142694 chr3 48694534 cg15142694 NA Island CELSR3
cg15130211 chr3 128276056 cg15130211 NA S_Shore
cg17350432 chr4 841569 cg17350432 NA N_Shore
cg13649728 chr4 128651707 cg13649728 NA Island SLC25A31
cg23110027 chr4 176394153 cg23110027 rs77206097 OpenSea
cg01042202 chr5 140242159 cg01042202 NA Island PCDHA6;PCDHA2;PCDHA1;PCDHA9;PCDHA7;PCDHA1;PCDHA6;PCDHA5;PCDHA10;PCDHA3;PCDHA4;PCDHA10;PCDHA8
cg01604946 chr5 148398804 cg01604946 NA OpenSea SH3TC2
cg15740979 chr5 176958383 cg15740979 NA Island FAM193B;FAM193B
cg02647297 chr6 3867369 cg02647297 NA OpenSea
cg24328676 chr6 32134970 cg24328676 NA Island EGFL8
cg19939773 chr6 32729876 cg19939773 NA Island HLA-DQB2
cg23120936 chr6 44251344 cg23120936 NA N_Shelf TCTE1
cg08882882 chr6 84937375 cg08882882 NA Island KIAA1009
cg16727231 chr6 139485336 cg16727231 NA N_Shelf HECA
cg16362592 chr7 35289568 cg16362592 NA N_Shelf TBX20;TBX20
cg19083626 chr7 55322087 cg19083626 NA N_Shore
cg01709543 chr7 98592411 cg01709543 NA OpenSea TRRAP
cg12616177 chr7 100434510 cg12616177 NA N_Shore
cg26981432 chr8 23307949 cg26981432 NA OpenSea ENTPD4;ENTPD4
cg21040069 chr8 145732410 cg21040069 rs45592435 N_Shore GPT
cg20453969 chr10 27541301 cg20453969 NA Island LOC387646
cg18576552 chr10 44434381 cg18576552 NA OpenSea
cg07064673 chr11 1491308 cg07064673 rs62623399 Island HCCA2
cg09371112 chr11 12222570 cg09371112 NA OpenSea MICAL2
cg08013331 chr12 56040208 cg08013331 rs77625892 Island
cg00390143 chr12 132842539 cg00390143 NA Island GALNT9
cg07601148 chr13 20975917 cg07601148 NA OpenSea
cg19916129 chr13 113242878 cg19916129 NA S_Shore TUBGCP3
cg16466870 chr14 101926959 cg16466870 NA S_Shore
cg14410733 chr15 39624999 cg14410733 NA OpenSea
cg07375207 chr16 717419 cg07375207 NA N_Shore RHOT2;WDR90
cg02223028 chr16 30536135 cg02223028 NA Island ZNF768
cg26612794 chr16 88148745 cg26612794 rs79104167 OpenSea
cg27578381 chr17 76814686 cg27578381 NA OpenSea USP36
cg27107970 chr17 79520734 cg27107970 NA S_Shore C17orf70;C17orf70
cg14894245 chr19 1106640 cg14894245 NA N_Shore GPX4;GPX4;GPX4
cg23466054 chr19 22018892 cg23466054 NA S_Shore ZNF43;ZNF43
cg24282826 chr21 35288546 cg24282826 NA S_Shore ATP5O

Metabolite at PSV

There are 2 pairs with significant NIE:

Pair NIE
cg02050985 & lipid_329 275.050
cg21507958 & hilic_397 18.454
cg21507958 & hilic_1012 12.706
cg26428191 & hilic_1012 8.024
cg26378982 & lipid_931 3.504
cg10494860 & hilic_1012 2.484
cg16469223 & lipid_386 2.031
cg24115232 & lipid_563 0.542
cg16805215 & lipid_294 0.540
cg24998815 & lipid_572 0.001
cg24539295 & hilic_1012 0.000

Data issues

Same for this structure:

When the methylation values are also scaled, the NIE value is much more reasonable:

x
cde 2.3729446
pnde 2.2986127
tnie 0.9345334
tnde 1.9415763
pnie 1.1063847
te 2.1481303

Next pair:

x
cde 3.4546734
pnde 2.5719766
tnie 0.9430224
tnde 2.2068527
pnie 1.0990455
te 2.4254316

Annotation

feature name
683 hilic_397 Unknown
1298 hilic_1012 Unknown
1612 lipid_294 Unknown
1647 lipid_329 Unknown
1704 lipid_386 Unknown
1881 lipid_563 FA (12:0) [M-H]- (lauric acid)_POULHZVOKOAJMA-UHFFFAOYSA-N
1890 lipid_572 FA (18:0) [M-H]- (stearic acid)_QIQXTHQIDYTFRH-UHFFFAOYSA-N
2249 lipid_931 Unknown
chr pos Name Probe_rs Relation_to_Island UCSC_RefGene_Name
cg26428191 chr1 185380011 cg26428191 NA OpenSea
cg26378982 chr2 11053937 cg26378982 NA Island KCNF1
cg02050985 chr2 101766314 cg02050985 NA N_Shore TBC1D8
cg16805215 chr3 137505160 cg16805215 NA OpenSea
cg16469223 chr3 184095245 cg16469223 NA N_Shelf THPO
cg24115232 chr5 1243907 cg24115232 NA Island SLC6A18
cg24539295 chr13 24462942 cg24539295 NA N_Shore PCOTH;PCOTH;MIPEP
cg24998815 chr14 90798128 cg24998815 NA N_Shore C14orf102;C14orf102
cg21507958 chr17 78818871 cg21507958 NA S_Shore RPTOR;RPTOR
cg10494860 chr20 62693951 cg10494860 NA Island TCEA2;TCEA2